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Register a new userHolographic 2-Point Functions in the Pseudo-Conformal Universe
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We holographically calculate two-point functions in the pseudo-conformal universe, an early universe alternative to inflation. The pseudo-conformal universe can be modeled as a defect conformal field theory, where the reheating surface is a codimension-1 spacelike defect which breaks the conformal algebra to a de Sitter subalgebra. The dual spacetime geometries are domain walls with de-Sitter symmetry in an asymptotically anti-de Sitter spacetime. We compute 2-point functions of scalars and stress tensors by solving the linearized equations for scalar and tensor fluctuations about these backgrounds.
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The recently developed gauge-invariant formalism for the treatment of fluctuations in holographic renormalization group (RG) flows overcomes most of the previously encountered technical difficulties. I summarize the formalism and present its application to the GPPZ flow, where scattering amplitudes between glueball states have been calculated and a set of selection rules been found.
We develop the formalism of holographic renormalization to compute two-point functions in a holographic Kondo model. The model describes a $(0+1)$-dimensional impurity spin of a gauged $SU(N)$ interacting with a $(1+1)$-dimensional, large-$N$, strongly-coupled Conformal Field Theory (CFT). We describe the impurity using Abrikosov pseudo-fermions, and define an $SU(N)$-invariant scalar operator $mathcal{O}$ built from a pseudo-fermion and a CFT fermion. At large $N$ the Kondo interaction is of the form $mathcal{O}^{dagger} mathcal{O}$, which is marginally relevant, and generates a Renormalization Group (RG) flow at the impurity. A second-order mean-field phase transition occurs in which $mathcal{O}$ condenses below a critical temperature, leading to the Kondo effect, including screening of the impurity. Via holography, the phase transition is dual to holographic superconductivity in $(1+1)$-dimensional Anti-de Sitter space. At all temperatures, spectral functions of $mathcal{O}$ exhibit a Fano resonance, characteristic of a continuum of states interacting with an isolated resonance. In contrast to Fano resonances observed for example in quantum dots, our continuum and resonance arise from a $(0+1)$-dimensional UV fixed point and RG flow, respectively. In the low-temperature phase, the resonance comes from a pole in the Greens function of the form $-i langle {cal O} rangle^2$, which is characteristic of a Kondo resonance.
We exploit a gauge invariant approach for the analysis of the equations governing the dynamics of active scalar fluctuations coupled to the fluctuations of the metric along holographic RG flows. In the present approach, a second order ODE for the active scalar emerges rather simply and makes it possible to use the Greens function method to deal with (quadratic) interaction terms. We thus fill a gap for active scalar operators, whose three-point functions have been inaccessible so far, and derive a general, explicitly Bose symmetric formula thereof. As an application we compute the relevant three-point function along the GPPZ flow and extract the irreducible trilinear couplings of the corresponding superglueballs by amputating the external legs on-shell.
For holographic CFT states near the vacuum, entanglement entropies for spatial subsystems can be expressed perturbatively as an expansion in the one-point functions of local operators dual to light bulk fields. Using the connection between quantum Fisher information for CFT states and canonical energy for the dual spacetimes, we describe a general formula for this expansion up to second-order in the one-point functions, for an arbitrary ball-shaped region, extending the first-order result given by the entanglement first law. For two-dimensional CFTs, we use this to derive a completely explicit formula for the second-order contribution to the entanglement entropy from the stress tensor. We show that this stress tensor formula can be reproduced by a direct CFT calculation for states related to the vacuum by a local conformal transformation. This result can also be reproduced via the perturbative solution to a non-linear scalar wave equation on an auxiliary de Sitter spacetime, extending the first-order result in arXiv/1509.00113.
We apply the analytic conformal bootstrap method to study weakly coupled conformal gauge theories in four dimensions. We employ twist conformal blocks to find the most general form of the one-loop four-point correlation function of identical scalar operators, without any reference to Feynman calculations. The method relies only on symmetries of the model. In particular, it does not require introducing any regularisation and it is free from the redundancies usually associated with the Feynman approach. By supplementing the general solution with known data for a small number of operators, we recover explicit forms of one-loop correlation functions of four Konishi operators as well as of four half-BPS operators $mathcal{O}_{20}$ in $mathcal{N}=4$ super Yang-Mills.
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